Pairwise Clustering with Matrix Factorisation and the EM Algorithm

Abstract

In this paper we provide a direct link between the EM algorithm and matrix factorisation methods for grouping via pairwise clustering. We commence by placing the pairwise clustering process in the setting of the EM algorithm. We represent the clustering process using two sets of variables which need to be estimated. The first of these are cluster-membership indicators. The second are revised link-weights between pairs of nodes. We work with a model of the grouping process in which both sets of variables are drawn from a Bernoulli distribution. The main contributioin in this paper is to show how the cluster-memberships may be estimated using the leading eigenvector of the revised link-weight matrices. We also establish convergence conditions for the resulting pair-wise clustering process. The method is demonstrated on the problem of multiple moving object segmentation.